I have the same problem with installing Lastpass, I also have version: Chromium: 70.0.3538.54 (Official Build) beta (64-bit).
Unfortunately I can’t seem to update to 0.55.18 either, going through menu->About Brave.
I noticed there was someone else in another thread just recently who also had problems with updating Brave.
After reading this thread I’m hesitant about installing 0.55.18 by downloading the binaries, I don’t want to lose any settings etc.
I’ll wait a couple of days before trying again and try to live with the inconvenience.
I Just thought you should know.
Thanks for all your efforts, you’re doing a great job.
*** EDIT ***
I get the following status when trying to update Brave in-browser:
An error occurred while checking for updates: Installationen misslyckades. Försök igen. (error code 7: 0xA043090B – system level).